Maxima

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Maxima branch_5_30_base_104_ged70fb2_dirty http://maxima.sourceforge.net
using Lisp SBCL 1.0.45.0.debian
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1)

"Maxima's current array/matrix semantics are a mess, I must say, with at least four different kinds of object (hasharrays, explicit lists, explicit matrices, Lisp arrays) supporting subscripting with varying semantics. " [9]

"If the user assigns to a subscripted variable before declaring the corresponding array, an undeclared array is created. Undeclared arrays, otherwise known as hashed arrays (because hash coding is done on the subscripts), are more general than declared arrays. The user does not declare their maximum size, and they grow dynamically by hashing as more elements are assigned values. The subscripts of undeclared arrays need not even be numbers. However, unless an array is rather sparse, it is probably more efficient to declare it when possible than to leave it undeclared. " ( from Maxima CAS doc)

"created if one does :

b[x+1]:y^2

(and b is not already an array, a list, or a matrix - if it were one of these an error would be caused since x+1 would not be a valid subscript for an art-q array, a list or a matrix).

Its indices (also known as keys) may be any object. It only takes one key at a time (b[x+1,u]:y would ignore the u). Referencing is done by b[x+1] ==> y^2. Of course the key may be a list, e.g.

The advantage of make_array over array is that the return value doesn't have a name, and once a pointer to it goes away, it will also go away. For example, if y: make_array (...) then y points to an object which takes up space, but after y: false, y no longer points to that object, so the object can be garbage collected.

"The dot operator, for matrix (non-commutative) multiplication. When "." is used in this way, spaces should be left on both sides of it, e.g.

A . B

This distinguishes it plainly from a decimal point in a floating point number.

The operator . represents noncommutative multiplication and scalar product. When the operands are 1-column or 1-row matrices a and b, the expression a.b is equivalent to sum (a[i]*b[i], i, 1, length(a)). If a and b are not complex, this is the scalar product, also called the inner product or dot product, of a and b. The scalar product is defined as conjugate(a).b when a and b are complex; innerproduct in the eigen package provides the complex scalar product.

When the operands are more general matrices, the product is the matrix product a and b. The number of rows of b must equal the number of columns of a, and the result has number of rows equal to the number of rows of a and number of columns equal to the number of columns of b.

To distinguish . as an arithmetic operator from the decimal point in a floating point number, it may be necessary to leave spaces on either side. For example, 5.e3 is 5000.0 but 5 . e3 is 5 times e3.